New Lower Bounds on the Generalized Hamming Weights of AG Codes

被引：18

作者：

Bras-Amoros, Maria ^{[1
]}

Lee, Kwankyu ^{[2
]}

Vico-Oton, Albert ^{[1
]}

机构：

[1] Univ Rovira & Virgili, Dept Comp Engn & Math, E-43007 Tarragona, Catalonia, Spain

[2] Chosun Univ, Dept Math & Educ, Kwangju 501759, South Korea

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2014年 / 60卷 / 10期

基金：

新加坡国家研究基金会;

关键词：

Numerical semigroup; ideal of a semigroup; AG code; isometry-dual sets of AG codes; generalized Hamming weights; order bound; Feng-Rao number; Hermitian codes; Garcia-Stichtenoth towers; MINIMUM DISTANCE; WEIERSTRASS SEMIGROUPS; HIERARCHY;

D O I：

10.1109/TIT.2014.2343993

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A sharp upper bound for the maximum integer not belonging to an ideal of a numerical semigroup is given and the ideals attaining this bound are characterized. Then, the result is used, through the so-called Feng-Rao numbers, to bound the generalized Hamming weights of algebraic-geometry codes. This is further developed for Hermitian codes and the codes on one of the Garcia-Stichtenoth towers, as well as for some more general families.

引用

页码：5930 / 5937

页数：8

共 40 条

[1] The weight hierarchy of Hermitian codes [J].

Barbero, AI ;

Munuera, C .

SIAM JOURNAL ON DISCRETE MATHEMATICS, 2000, 13 (01) :79-104

[2] DECOMPOSITIONS OF IDEALS INTO IRREDUCIBLE IDEALS IN NUMERICAL SEMIGROUPS [J].

Barucci, Valentina .

JOURNAL OF COMMUTATIVE ALGEBRA, 2010, 2 (03) :281-294

[3] Acute semigroups, the order bound on the minimum distance, and the Feng-Rao improvements [J].

Bras-Amorós, M .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (06) :1282-1289

[4]

Bras-Amoros M., 2014, P AC CONT FOR GAL GE, P69

[5] The order bound on the minimum distance of the one-point codes associated to the Garcia-Stichtenoth tower [J].

Bras-Amoros, Maria ;

O'Sullivan, Michael E. .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2007, 53 (11) :4241-4245

[6] Semigroups generated by two consecutive integers and improved hermitian codes [J].

Bras-Amoros, Maria ;

O'Sullivan, Michael E. .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2007, 53 (07) :2560-2566

[7] A note on numerical semigroups [J].

Bras-Amoros, Maria .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2007, 53 (02) :821-823

[8] Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models [J].

Campillo, A ;

Farrán, JI .

FINITE FIELDS AND THEIR APPLICATIONS, 2000, 6 (01) :71-92

[9] Some new codes from algebraic curves [J].

Ding, Cunsheng ;

Niederreiter, Harald ;

Xing, Chaoping .

2000, IEEE, Piscataway, NJ, United States (46)

[10]

dela Cruz R., 2010, P IEEE INF THEOR WOR

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